Up to four million people are expected to have visited the installation, Blood Swept Lands And Seas Of Red by ceramic artist Paul Cummins, before it is dismantled on November 12.

However Lord Dannatt, the most senior official at the Tower of London and the former head of the army, said that although he understands the “pressure” to keep the monument open plans to dismantle it could not change at this stage.

Nick Clegg said the memorial allowed people to feel “connected to our history” and “trace their own family’s history to this huge act of national self-sacrifice”.

The Deputy Prime Minister told his LBC radio show: “I haven’t seen it, I have seen obviously the photos and spoken to people who have been to see it, and it obviously really struck a chord, it’s extraordinary, and very moving to see. And so much so did you see last week the local underground station at Tower Hill was closed because so many people were going to see it.

“I think in a sense it is speaking to something very profound in people, that people want to be connected to our history, they want to trace their own family's history to this huge act of national self-sacrifice at the time of the First World War and these ceramic poppies have really come to symbolise that.

The Queen and Duke of Edinburgh visit the installation ( Geoff Pugh/The Telegraph)

“Now I would love to see it carry on further, my understanding however is that each individual poppy is being sold and the proceeds of those sales, and I think there are thousands of volunteers are at the moment at least scheduled to come on the 12th to package up each individual poppy so that they can be given to a number of people who have bought them.

"And that money is going to a number of charities that help service personnel who have suffered injuries in conflict.

“So let’s try and get the balance right. Let’s keep the display going a bit longer but not deprive those charities of that much needed money from the poppies.

Officials at the Royal Palaces, which is running the memorial, said that they have a responsibility to get the ceramic poppies to those who have purchased them as quickly as possible.

“The poppies need to be removed to a factory, cleaned before they can be sent out. The size of the “logistical operation” means that it is not feasible to extend the run of memorial.”

George Osborne has announced this week that the Government will waive the expected VAT of up to £1.1 million from sales of the poppies.

David Cameron said yesterday that the “extraordinary project” has “brought forward from the British public a huge amount of reverence for those who have given their lives and served our country.”